Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for a town i

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Let X Be A Random Variable That Represents The Average Daily Temperature In Degrees Fahrenheit In January For A Town I 1 (72.21 KiB) Viewed 20 times

Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for a town in Hawaii. The x variable has a mean u of approximately 68°F and standard deviation o of approximately 4°F. A 20-year study (620 January days) gave the entries in the rightmost column of the following table. II III IV Region under Normal Expected % from Observed Number of X°F Curve Normal Curve Days in 20 Years μ - 3σχ<μ - 2σ 56 < X < 60 2.35% 20 μ – 2σχ<μ – σ 60 SX < 64 13.5% 86 u-OSX<u 64 SX < 68 34% 211 μχ <μ +σ 68 < X < 72 34% 209 μ +σχ <μ + 2σ 72 3 x < 76 13.5% 81 u + 20 <x< u + 30 76 < X < 80 2.35% 13 (i) Remember that u = 68 and o = 4. Examine the Normal Distribution Curve. Write a brief explanation for columns I, II, and III in the context of this problem. 4. (ii) Use a 1% level of significance to test the hat the average daily January temperature follows a mal distributi with u = 68 and o You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) What is the level of significance? 0.01 State the null and alternate hypotheses. O Ho: The distributions are different. Hj: The distributions are the same. O Ho: The distributions are different. Hj: The distributions are different. O Ho: The distributions are the same. Hz: The distributions are different. O Ho: The distributions are the same. H: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.) Are all the expected frequencies greater than 5? O Yes O No What sampling distribution will you use? O uniform O Student's t O normal O chi-square O binomial What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) O p-value > 0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 O P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? O Since the P-value > a, we fail to reject the null hypothesis. Since the P-value > a, we reject the null hypothesis. Since the P-value sa, we reject the null hypothesis. O Since the P-value sa, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 1% level of significance, the evidence is sufficient to conclude that the average daily January temperature does not follow a normal distribution. O At the 1% level of significance, the evidence is insufficient to conclude that the average daily January temperature does not follow a normal distribution.